hydrostaticparametersanddomaineffectsinnovel2-2 ...downloads.hindawi.com/archive/2011/173064.pdf ·...

$: HydrostaticParametersandDomainEffectsinNovel2-2 ...downloads.hindawi.com/archive/2011/173064.pdf · Orientation and volume-fraction dependences of the hydrostatic ... (see insets$
Hindawi Publishing CorporationSmart Materials ResearchVolume 2011, Article ID 173064, 10 pagesdoi:10.1155/2011/173064

Research Article

Hydrostatic Parameters and Domain Effects in Novel 2-2Composites Based on PZN-0.12PT Single Crystals

Vitaly Yu. Topolov,1 Sergei V. Glushanin,2 and Alexander A. Panich2

1 Department of Physics, Southern Federal University, 5 Zorge Street, Rostov-on-Don 344090, Russia2 Scientific Design & Technology Institute “Piezopribor,” Southern Federal University, 10 Milchakov Street,Rostov-on-Don 344090, Russia

Correspondence should be addressed to Vitaly Yu. Topolov, [email protected]

Received 18 October 2010; Accepted 26 January 2011

Academic Editor: Zhifei Shi

Copyright © 2011 Vitaly Yu. Topolov et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

A novel 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystal/polymer composite with 2-2 connectivity is studied at variable orientationsof spontaneous polarisation vector of the crystal component. Orientation and volume-fraction dependences of the hydrostaticpiezoelectric coefficients d∗h , e∗h , and g∗h and hydrostatic electromechanical coupling factor k∗h are related to the important role ofthe piezoelectric and elastic anisotropy of single-domain layers of the 2-2 composite. The record value of |e∗h | ≈ 77 C/m2 nearthe absolute-minimum point and the correlation between the hydrostatic (e∗h ) and piezoelectric (e∗3 j) coefficients and between thehydrostatic (g∗h ) and piezoelectric (g∗3 j) coefficients are first established. This discovery is of value for hydrostatic and piezotechnicalapplications. The hydrostatic performance of the composite based on the single-domain 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystalis compared to the performance of the 2–2 composites based on either the same polydomain crystal or the related single-domaincrystal.

1. Introduction

The polarisation orientation effect in advanced piezo-activecomposites based on relaxor-ferroelectric single crystals(SCs) of (1 − x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-xPT)[1–3] and (1 − y)Pb(Mg1/3Nb2/3)O3-yPbTiO3 (PMN-yPT)[3, 4] opens up new possibilities of the variation ofeffective parameters of the composites that are of valuefor modern hydroacoustic and piezotechnical applications.The anisotropic SC component with large piezoelectric

coefficients (e.g., d(1)3 j ∼ 103 pC/N, hereafter we use

superscript “(1)” to denote electromechanical constantsof the SC component) [5, 6] plays an important rolein forming the piezoelectric effect of the composite andits hydrostatic piezoelectric response, as shown in recentpapers on the 2-2 [1, 3, 4] and 1-3 [2] SC/polymercomposites. The 2-2 parallel-connected composite based onthe single-domain PMN-0.33PT SC [4] is an example of apiezoelectric material whereby large hydrostatic piezoelectriccoefficients are achieved at specific orientations of the

crystallographic axes and SC volume fraction. As is known,the chemical composition of PMN-0.33PT is located nearthe morphotropic phase boundary, and the PMN-0.33PTSC in the single-domain state is described by 3m symmetryat room temperature [7]. Along with electromechanicalconstants of PMN-0.33PT, there are complete sets of room-temperature electromechanical constants (Table 1) measuredon the single-domain PMN-0.42PT [5] and PZN-0.12PT [8]SCs with 4mm symmetry. We see the difference between

the piezoelectric coefficients d(1)i j of PMN-0.42PT and PZN-

0.12PT SCs, for which the order of magnitude of d(1)i j

remains 102 pC/N (Table 1). We note that the single-domainPZN-0.12PT SC exhibits a distinctive elastic anisotropy incomparison to that of the single-domain PMN-0.42PT SC:according to data from Table 1, ratios

s(1),E33

s(1),E11

= 2.71,s(1),E

11∣∣∣s(1),E

13

∣∣∣

= 1.10 (1)

2 Smart Materials Research

Table 1: Elastic compliances s(n),Eab (in 10−12 Pa−1), piezoelectric coefficients d(n)

i j (in pC/N), and relative dielectric permittivity ε(n),σpp /ε0 of

single-domain SC and polymer components at room temperature.

Components s(n),E11 s(n),E

12 s(n),E13 s(n),E

33 s(n),E44 s(n),E

66

PZN-0.12PT SC [8] 20.1 −4.6 −18.2 54.5 19.5 17.2

PMN-0.42PT SC [5] 9.43 −1.68 −6.13 19.21 35.09 12.5

Polyurethane [11] 400 −148 −148 400 1100 1100

Components d(n)31 d(n)

33 d(n)15 ε(n),σ

11 /ε0 ε(n),σ33 /ε0

PZN-0.12PT SC [8] −207 541 653 10000 750

PMN-0.42PT SC [5] −91 260 131 8627 660

Polyurethane [11] 0 0 0 3.5 3.5

are valid for PZN-0.12PT. At the same time, the single-domain SCs are characterised by the almost equal anisotropy

of d(1)3 j : as follows from Table 1,

d(1)33

∣∣∣d(1)

31

∣∣∣

= 2.61(PZN-0.12PT),

d(1)33

∣∣∣d(1)

31

∣∣∣

= 2.86(PMN-0.42PT).

(2)

The distinctions shown in (1) could influence the piezo-electric effect and hydrostatic response of the composite,and such an effect has not been considered in detail inearlier studies. In this work, we first study the domaineffects concerned with the polarisation orientation and thehydrostatic response of the 2-2 SC/polymer composite in awide volume fraction and orientation ranges. The aim ofthe present paper is to show the role of the domain effectsand the electromechanical properties of SCs in developinga considerable hydrostatic response of the 2-2 composite(with either single-domain or polydomain layers). Belowwe discuss some advantages concerned with the hydrostaticpiezoelectric coefficients of the composite based on thesingle-domain PZN-0.12PT SC.

2. Structure and Effective ElectromechanicalProperties of the 2-2 Composite

It is assumed that the composite represents a system of theparallel-connected SC and polymer layers which form theregular laminar structure (Figure 1) with 2-2 connectivity(in terms of [9]). The crystallographic axes X , Y , and Zof the single-domain SC in the initial state (α = 0 orβ = 0; see insets 1 and 2 in Figure 1) are parallel tothe following perovskite unit-cell directions: X‖[100]‖OX1,Y‖[010]‖OX2, and Z‖[001]‖OX3. In this case, the sponta-neous polarization vector in each SC layer is P(1)

s ‖OX3. We

consider rotations of the P(1)s vector around one of the co-

ordinate axes—OX1 or OX2 (see insets 1 and 2 in Figure 1),and all the SC layers in the composite sample have the same

orientation of P(1)s . Thus, a system of SC cuts with a fixed

orientation of the crystallographic axes X , Y , and Z is to be

prepared before manufacturing the 2-2 composite sample.The orientation of the crystallographic axes in the alignedcuts can be checked by means of X-ray technique, and thefurther poling procedure is assumed to be performed at thefixed orientation of the composite sample as a whole. Thesingle-domain state of the SC layers (cuts) in the samplecan be stabilised under bias. In a polydomain SC layer,the rotation of the effective spontaneous polarisation vector

P(1,polyd)s = mdPs,1 + (1 − md)Ps,2 in the (X2OX3) plane is

caused by changes in the volume fraction md of the laminar90◦ domains (inset 3 in Figure 1), and these changes can becaused by an external electric field that is initially applied tothe SC layers.

The effective electromechanical properties of the 2-2composite are studied within the framework of the matrixapproach [10] that is applied to composite materials withplanar microgeometry. The 9 × 9 matrix of the effectiveproperties of the composite in the rectangular co-ordinatesystem (X1X2X3)

∥∥C∗

∥∥ =

⎛

⎝

∥∥s∗E

∥∥ ‖d∗‖t

‖d∗‖ ‖ε∗σ‖

⎞

⎠ (3)

is written in terms of ‖s∗E‖ (6 × 6 matrix of elasticcompliances at constant electric field), ‖d∗‖ (3 × 6 matrixof piezoelectric charge coefficients), and ‖ε∗σ‖ (3× 3 matrixof dielectric permittivities measured at constant stress),where superscript “t” denotes the transposed matrix. The‖C∗‖ matrix from (3) is determined from averaging theelectromechanical properties of components on the volumefraction m and is given by

∥∥C∗

∥∥ =

[∥∥∥C(1)

∥∥∥ · ‖M‖m +

∥∥∥C(2)

∥∥∥(1−m)

]

· [‖M‖m + ‖I‖(1−m)]−1,(4)

where ‖C(1)‖ and ‖C(2)‖ are matrices of the electrome-chanical properties of SC and polymer, respectively, ‖M‖is concerned with the electric and mechanical boundaryconditions [10] at interfaces x1 = const (Figure 1), and ‖I‖is the identity 9 × 9 matrix. Elements of the ‖C(1)‖ matrix

are written taking into account the orientation of P(1)s in the

single-domain SC layer (insets 1 and 2 in Figure 1) or thevolume fraction md of the 90◦ domains (inset 3 in Figure 1).

Smart Materials Research 3

X1

X1

X1

X2

X2X2

Polymer, volumefraction 1−m

0

0 0

0

md

1−md

1 2 3X′1

X′3

X′3

X3

β

X2 = X′2

P(1)s

P(1)s

X1 = X′1

α

X3

X3

X3X′2

Single crystal,volume fraction m

Figure 1: Schematic of the 2-2 parallel-connected SC/polymer composite. (X1X2X3) is the rectangular co-ordinate system of the compositesample α and β are angles of rotation of the spontaneous polarisation vector P(1)

s ‖OX ′3 of the single-domain SC layer around the OX1 axis

(inset 1) or around the OX2 axis (inset 2). In inset 3 the 90◦ domain structure in the SC layer is schematically shown, where md and 1−md

are volume fractions of the 90◦ domains in the SC layer, and their spontaneous polarisation vectors are shown with arrows.

In case of the single-domain SC layer, the elements

of ‖C(1)‖ are represented in the tensor form as ε(1),σnp =

rnkrpl(ε(1),σkl )T , d(1)

i f g = ritr f urgv(d(1)tuv)T , and s(1),E

pqvw =rpcrqlrvhrwn(s(1),E

clhn )T , where rnk is the element of the matrix

that describes the rotation of the P(1)s vector and the co-

ordinate axes, and subscript “T” means that the electrome-chanical constant is given in the main crystallographic axes,that is, taken from Table 1. The aforementioned rotation isshown in either inset 1 in Figure 1 (then rnk is represented inthe general form as rnk = rnk(α)) or inset 2 in Figure 1 (thenin the general form rnk = rnk(β)). In the case of a polydomainSC layer (inset 3 in Figure 1), the rotation of the co-ordinateaxes by α = ±45◦ in the adjacent domains is to be takeninto account in the matrix elements rnk, rpl, and so forth. Theeffective electromechanical properties of the polydomain SClayer in the co-ordinate system (X1X2X3) are determined byanalogy with (4)

∥∥∥C(1)

∥∥∥ =

[∥∥∥C(d1)

∥∥∥ · ‖Md‖md +

∥∥∥C(d2)

∥∥∥(1−md)

]

· [‖Md‖md + ‖I‖(1−md)]−1,(5)

where ‖C(d1)‖ and ‖C(d2)‖ are matrices of electromechanicalconstants of the 90◦ domains with the volume fractions md

and 1 −md, respectively, and ‖Md‖ is the matrix concerned

with the boundary conditions [10] for elastic and electricfields at the domain wall x3 = const. The matrix from (5)is represented in the general form by

∥∥∥C(1)

∥∥∥

=

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

s(1),E11 s(1),E

12 s(1),E13 s(1),E

14 0 0 0 d(1)21 d(1)

31

s(1),E12 s(1),E

22 s(1),E23 s(1),E

24 0 0 0 d(1)22 d(1)

32

s(1),E13 s(1),E

23 s(1),E33 s(1),E

34 0 0 0 d(1)23 d(1)

33

s(1),E14 s(1),E

24 s(1),E34 s(1),E

44 0 0 0 d(1)24 d(1)

34

0 0 0 0 s(1),E55 s(1),E

56 d(1)15 0 0

0 0 0 0 s(1),E56 s(1),E

66 d(1)16 0 0

0 0 0 0 d(1)15 d(1)

16 ε(1),σ11 0 0

d(1)21 d(1)

22 d(1)23 d(1)

24 0 0 0 ε(1),σ22 ε(1),σ

23

d(1)31 d(1)

32 d(1)33 d(1)

34 0 0 0 ε(1),σ23 ε(1),σ

33

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

.

(6)

It should be added that the electromechanical properties ofthe polydomain PZN-0.12PT SC were also calculated in [8].


The ‖M‖ matrix from (4) is determined [10] with dueregard for the boundary conditions at the layer interfacesx1 = const as follows: ‖M‖ = ‖W1‖−1 · ‖W2‖, where

‖Wn‖

=

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 0 0 0 0 0 0 0 0

s(n),E12 s(n),E

22 s(n),E23 s(n),E

24 s(n),E25 s(n),E

26 d(n)12 d(n)

22 d(n)32

s(n),E13 s(n),E

23 s(n),E33 s(n),E

34 s(n),E35 s(n),E

36 d(n)13 d(n)

23 d(n)33

s(n),E14 s(n),E

24 s(n),E34 s(n),E

44 s(n),E45 s(n),E

46 d(n)14 d(n)

24 d(n)34

0 0 0 0 1 0 0 0 0

0 0 0 0 0 1 0 0 0

d(n)11 d(n)

12 d(n)13 d(n)

14 d(n)15 d(n)

16 ε(n),σ11 ε(n),σ

12 ε(n),σ13

0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 1

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

,

(7)

n = 1 is related to SC, and n = 2 is related to polymer.The effective electromechanical properties of the composite(‖C∗‖ from (4)) and the polydomain layer (‖C(1)‖ from (5))are determined on an assumption that the wavelengths ofacoustic waves propagated are considerably longer than thethickness of each layer in the composite sample (Figure 1),and the thickness of each domain (see inset 3 in Figure 1) ismuch less than the height of the polydomain layer.

Based on matrix elements of ‖C∗‖ from (4), we studythe volume fraction and orientation dependences of thehydrostatic piezoelectric coefficients

d∗h = d∗31 + d∗32 + d∗33,

g∗h = g∗31 + g∗32 + g∗33,

e∗h = e∗31 + e∗32 + e∗33,

(8)

and hydrostatic electromechanical coupling factor of thecomposite

k∗h =d∗h

√

s∗Eh ε∗σ33

. (9)

The piezoelectric coefficients g∗i j from (8) are determined

from the matrix ‖g∗‖ = ‖d∗‖ · ‖ε∗σ‖−1 the piezoelectriccoefficients e∗i j from (8) are determined from the matrix

‖e∗‖ = ‖d∗‖ · ‖s∗E‖−1. Hydrostatic compliance s∗Eh of the

composite at E = const (see (9)) is defined as follows:s∗Eh = ∑3

a=1

∑3b=1 s

∗Eab . The hydrostatic parameters Φ∗

h from(8) and (9) characterise the performance of the compositesample (Figure 1) with electrodes that are parallel to the(X1OX2) plane. The effective electromechanical properties ofthe polydomain SC layer (inset 3, Figure 1), the compositeas a whole (see (4)), and its hydrostatic parameters (see (8)

and (9)) are calculated using the full sets of experimentalelectromechanical constants from Table 1.

3. Hydrostatic Parameters and Advantages

Examples of the calculated volume-fraction and orienta-tion dependences of the hydrostatic parameters Φ∗

h of thecomposite based on the single-domain PZN-0.12PT SCare shown in Figures 2 and 3. The presence of SC with4mm symmetry and polymer with ∞mm symmetry enablesus to establish the periodic dependence of the hydrostaticparameters on the rotation angles α and β. For any valueof m from the range 0 < m < 1, the equalities Φ∗

h (m,α) =Φ∗

h (m, 180◦ − α) and Φ∗h (m,β) = Φ∗

h (m,−β) hold, where0◦ ≤ α < 90◦ and 0◦ ≤ β < 90◦.

Changes in the orientation of the P(1)s vector of the

SC layer in the (X2OX3) plane (inset 1 in Figure 1) mean

changes in projections of P(1)s on the OX2 and OX3 axes,

along which both the components of the composite aredistributed continuously. Such a mode of rotation of the

P(1)s vector leads to a relatively smooth dependence of the

hydrostatic parameters Φ∗h on α (Figure 2). The hydrostatic

piezoelectric coefficient d∗h of the composite (Figure 2(a))

remains less than d(1)h of the single-domain SC. A combina-

tion of the piezoelectric (d∗i j ) and dielectric (ε∗σpp ) propertiesgives rise to the pronounced maxima of g∗h at α = const(Figure 2(b)) however, these maxima take place at a smallvolume fraction m. In (Figure 2(b)), we omit the volume-fraction range 0.1 < m < 1 where g∗h monotonicallydecreases at α = const. Combining the piezoelectric (d∗i j ) and

elastic (s∗Eab ) properties, one can attain the nonmonotonicvolume-fraction behaviour of the hydrostatic piezoelectriccoefficient e∗h (Figure 2(c)) however, values of e∗h near thelocal maximum points are relatively small. The complicatedshape of the surface of k∗h (m, α) (Figure 2(d)) is a result ofthe active influence of the dielectric properties at 0 < m < 0.1and of the elastic properties at 0.4 < m < 0.9. As follows fromthe comparison of the k∗h (m, α) and d∗h (m, α) dependences,there is a correlation between them in certain ranges of mand α. It should be noted that this correlation stems from (9)and is concerned with the relatively smooth dependence ofs∗Eh and ε∗σ33 on m and α.

The related composite based on the polydomain SC(see inset 3 in Figure 1) is characterised by the hydrostaticparameters varying in the fairly narrow ranges (Table 2). Thepolydomain SC layers have fixed orientations and volumefractions (md and 1 − md) of the 90◦ domains over thewhole composite sample, and a change in md means arotation of the effective spontaneous polarisation vector

P(1, polyd)s in the (X2OX3) plane. As in the previous case

of the single-domain SC layer, this rotation does not leadto considerable hydrostatic parameters. In our evaluations,the 90◦ domain walls of the polydomain SC layer areassumed to be motionless. A contribution from the 90◦

domain-wall displacements [12] provides a contributioninto electromechanical constants of SC. Our estimationsshow that this domain-wall contribution might give rise to


1530

4560

7590 0

0.20.4

0.60.8

10

20

40

60

80

100

120

140d∗ h

mα (deg)

(a)

m

g∗ h

00.02

0.040.06

0.080.1

0

50

100

150

200

1530

4560

7590

α (deg)

(b)

00.2

0.40.6

0.81

m

1530

4560

7590

α (deg)

0

1

2

3

4

e∗ h

(c)

k∗ h

0

0.05

0.1

0.15

0.2

0.25

0.3

00.2

0.40.6

0.81

m

1530

4560

7590

α (deg)

(d)

Figure 2: Hydrostatic piezoelectric coefficients (a)–(c) and electromechanical coupling factor (d) of the PZN-0.12PT SC/polyurethanecomposite at the rotation of the spontaneous polarisation vector P(1)

s of the single-domain SC layer around the OX1 axis (see inset 1 inFigure 1): (a) d∗h (in pC/N), (b) g∗h (in mV·m/N), (c) e∗h (in C/m2), and (d) k∗h .

increasing the upper bounds on Φ∗h (Table 2) by about 1.5–2

times.

Varying the angle β means the crossing of the spon-

taneous polarisation vector P(1)s of the single-domain SC

layer and the interface x1 = const (see inset 2 in Figure 1).

This mode of rotation of P(1)s becomes favourable to

achieve large values of hydrostatic parameters Φ∗h (m,β)

(Figure 3). In addition to the aforementioned combinationof the electromechanical properties, the anisotropy of elastic

compliances s(1),Eab of SC leads to increasing Φ∗

h in differ-ent volume-fraction ranges. Of particular interest is thehydrostatic piezoelectric coefficient e∗h (m,β) (Figure 3(c))with the deep absolute minimum. Recently [4], absolute

min e∗h = −44.4 C/m2 was found for the 2-2 PMN-0.33PTSC/polyvinylidene fluoride composite with the single-domain SC and piezo-active polymer layers. Distinctionsbetween PMN-0.33PT and PZN-0.12PT (both SCs in thesingle-domain state) are associated with both symmetry

[7, 8] and anisotropy of the electromechanical properties.As follows from experimental data on single-domain PMN-

0.33PT SCs with 3m symmetry [7], the ratios s(1),E11 /s(1),E

13 =−11.1, s(1),E

11 /s(1),E33 = 4.68, and d(1)

22 /d(1)33 = 7.05 hold in

the main crystallographic axes. The above circumstances areto be taken into account when comparing the compositeperformance. Undoubtedly, values of |e∗h | ≈ 77 C/m2

(Figure 3(c)) enable us to regard the studied 2-2 compositeas an outstanding piezoelectric material for hydroacousticapplications. To the best of our knowledge, in variousferroelectric ceramic/polymer composites [10], the typical e∗hvalues do not exceed 14 C/m2, and values of e∗h ≈ 10 C/m2

are peculiar to conventional poled ferroelectric ceramics atroom temperature [10, 13].

Our comparison of the performance of the compositesbased on single-domain SCs of PZN-0.12PT and PMN-0.42PT SCs (Table 3) suggests that the main differencebetween the hydrostatic parameters of these compositesis associated with the piezoelectric coefficients of the SCs


−150

−100

−50

0

50

100

150

200

β (deg)

d∗ h

015

3045

6075

90 00.2

0.40.6

0.81

m

(a)

g∗ h

−250−200

−150−100−50

0

50

100

150

200

250

m

00.02

0.040.06

0.080.1

β (deg)

015

3045

6075

90

(b)

−80

−60

−40

−20

0

e∗ h

β (deg)

015

3045

6075

90 00.2

0.40.6

0.81

m

(c)

k∗ h

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

β (deg)

015

3045

6075

90 00.2

0.40.6

0.81

m

(d)

Figure 3: Hydrostatic piezoelectric coefficients (a)–(c) and electromechanical coupling factor (d) of the PZN-0.12PT SC/polyurethanecomposite at the rotation of the spontaneous polarisation vector P(1)

s of the single-domain SC layer around the OX2 axis (see inset 2 inFigure 1): (a) d∗h (in pC/N), (b) g∗h (in mV·m/N), (c) e∗h (in C/m2), and (d) k∗h .

Table 2: Lower and upper bounds on hydrostatic parameters Φ∗h (m, md) of the PZN-0.12PT SC/polyurethane composite with polydomain

SC layers (see inset 3 in Figure 1) at 0 < m < 1 and md = const.

Φ∗h md = 0.1 and md = 0.9 md = 0.3 and md = 0.7 md = 0.5

d∗h (in pC/N) 0 < d∗h < 89.8 0 < d∗h < 89.8 0 < d∗h < 89.8

g∗h (in mV·m/N) 0 < g∗h < 10.6 0 < g∗h < 4.68 0 < g∗h < 1.89

e∗h (in C/m2) −0.816 < e∗h < 0.763 0 < e∗h < 7.81 0 < e∗h < 10.5

k∗h 0 < k∗h < 0.115 0 < k∗h < 0.115 0 < k∗h < 0.115

(Table 1). In addition, the hydrostatic piezoelectric coeffi-cient g∗h (see Table 3 and Figures 2(b) and 3(b)) at smallvolume fractions (0 < m < 0.1) strongly depends on thedielectric properties of components, while the hydrostaticpiezoelectric coefficient e∗h mainly depends on the anisotropyof the elastic properties of SC. It is clear that the anisotropy of

elastic compliances s(1),Eab of the single-domain PMN-0.42PT

SC is less pronounced (Table 1) and therefore do not lead to

the very large |e∗h | values in the composite based on this SC.As for the extreme values of g∗h , they are achieved at smallvolume fractions m and are of the same order of magnitudeas those studied in earlier papers [1, 3, 4, 10].

We also reveal an interesting correlation between thevolume-fraction dependences of the hydrostatic piezoelectriccoefficients and the piezoelectric coefficients that contributeto the hydrostatic response of the composite based on


Table 3: Extreme values of hydrostatic parameters Φ∗h (m,β) of 2-2 composites with single-domain SC layers (see inset 2 in Figure 1) at

0 < m < 1 and 0◦ ≤ β ≤ 90◦.

ParameterSingle-domain PZN-0.12PT SC/polyurethane composite Single-domain PMN-0.42PT SC/polyurethane composite

Absolute minima Absolute maxima Absolute minima Absolute maxima

d∗h−161 pC/N at m= 0.090and β = 78◦

214 pC/N at m = 0.972and β = 72◦

−69.9 pC/N at m = 0.081and β = 78◦

130 pC/N at m = 0.968and β = 72◦

g∗h−261 mV·m/N at m =0.005 and β = 71◦

215 mV·m/N at m = 0.028and β = 0◦

−821 mV·m/N at m = 0.005and β = 70◦

197 mV·m/N at m = 0.017and β = 0◦

e∗h−77.2 C/m2 at m = 0.825and β = 83◦

7.78 C/m2 at m = 0.768and β = 35◦

−28.6 C/m2 at m = 0.725and β = 79◦

10.2 C/m2 at m = 0.931and β = 0◦

k∗h−0.237 at m = 0.020and β = 74◦

—a −0.100 at m = 0.025and β = 74◦

0.144 at m = 0.063and β = 0◦

aThe largest value of k∗h corresponds to SC (m = 1).

0 0.2 0.4 0.6 0.8−80

−70

−60

−50

−40

−30

−20

−10

0

β = 80◦

m

e∗ 3j,e∗ h

e∗31e∗32

e∗33

e∗h

(a)

β = 83◦

0 0.2 0.4 0.6 0.8−80

−70

−60

−50

−40

−30

−20

−10

0

m

e∗ 3j,e∗ h

e∗31e∗32

e∗33

e∗h

(b)

β = 86◦

0 0.2 0.4 0.6 0.8−80

−70

−60

−50

−40

−30

−20

−10

0

m

e∗ 3j,e∗ h

e∗31e∗32

e∗33

e∗h

(c)

Figure 4: Correlation between piezoelectric coefficients e∗3 j and e∗h (in C/m2) of the PZN-0.12PT SC/polyurethane composite near absolutemin e∗h . The spontaneous polarisation vector P(1)

s of the single-domain SC layer is oriented as shown in inset 2 in Figure 1, the rotation angleβ = 80◦ (a), 83◦ (b) and 86◦ (c).


0 0.02 0.04 0.06 0.08 0.1−400

−300

−200

−100

0

100

200

300

β = 69◦

m

g∗ 3j,g∗ h

g∗31g∗32

g∗33g∗h

(a)

β = 71◦

0 0.02 0.04 0.06 0.08 0.1−400

−300

−200

−100

0

100

200

300

m

g∗ 3j,g∗ h

g∗31g∗32

g∗33g∗h

(b)

β = 73◦

0 0.02 0.04 0.06 0.08 0.1−400

−300

−200

−100

0

100

200

300

m

g∗ 3j,g∗ h

g∗31g∗32

g∗33g∗h

(c)

Figure 5: Correlation between piezoelectric coefficients g∗3 j and g∗h (in mV·m/N) of the PZN–0.12PT SC/polyurethane composite nearabsolute min g∗h . The spontaneous polarisation vector P(1)

s of the single-domain SC layer is oriented as shown in inset 2 in Figure 1, therotation angle β = 69◦ (a), 71◦ (b) and 73◦ (c).

PZN-0.12PT SC (see (8) and Figures 4 and 5). Graphs inFigure 4 show that, near the absolute minimum of e∗h , thepiezoelectric coefficients e∗3 j from (8) obey conditions

e∗32 ≈ e∗33,∣∣e∗33

∣∣ e∗31, (10)

that is, the presence of interfaces x1 = const weakensthe electromechanical interaction between the SC layers(Figure 1) and strongly influences the anisotropy of e∗3 j .Contrary to e∗3 j from Figure 4, the piezoelectric coefficientsg∗3 j from Figure 5 obey conditions

g∗31 ≈∣∣g∗32

∣∣, g∗33 ≈ g∗h . (11)

In our opinion, the distinctions between conditions (10) and(11) are associated with the different volume-fraction rangesof validity (e.g., large m values for e∗3 j and small m values forg∗3 j) and with the combination of the properties in the 2-2parallel-connected composite. In case of e∗3 j , the combinationof the piezoelectric and elastic properties plays the leadingrole, whereas behaviour of g∗3 j is accounted for by thecombination of the piezoelectric and dielectric properties.Graphs in Figure 5 suggest that large |g∗h | values can beattained at volume fractions of SC m ≈ 0.04–0.07, and thisrange is to be taken into consideration when manufacturingthe composite sample with high piezoelectric sensitivity. Ouranalysis of behaviour of the piezoelectric coefficients near theabsolute maxima (Figures 4 and 5) enables us to conclude


that not only the elastic and dielectric anisotropy, but alsothe parallel interfaces x1 = const in the composite sampleinfluence validity of conditions (10) and (11) in certainvolume-fraction and orientation ranges.

4. Conclusion

In this paper, we first studied features of the hydro-static piezoelectric response of the novel 2-2 PZN-0.12PTSC/polyurethane composite with parallel-connected layers.The considerable hydrostatic parameters and the anisotropyof the piezoelectric coefficients (see conditions (10) and (11))in the composite based on the single-domain PZN-0.12PTSC are strongly connected with peculiarities of its elasticand piezoelectric properties as well as with the orientationof the spontaneous polarisation vector P(1)

s with respect tothe interface x1 = const (Figure 1). The correlation betweenthe piezoelectric coefficients near the absolute minima ofthe hydrostatic parameters (Figures 4 and 5) is observed atdifferent conditions for the piezoelectric coefficients (cf. (10)and (11)), and such behaviour has no analogs among otherpiezo-active composites. In our opinion, the anisotropyof the piezoelectric and elastic properties of the single-domain SC indirectly could influence the volume-fractiondependence of the piezoelectric coefficients shown in Figures4 and 5.

The orientation effect studied in this paper enables usto conclude that the mutual arrangement of the interfacesand the spontaneous polarisation vectors of the SC layers(Figure 1) plays an important role in forming the significanthydrostatic response of the 2-2 parallel-connected compos-ite. The single-domain SC layers in the 2-2 composite studiedhave advantages over the polydomain layers mainly as theresult of the large hydrostatic piezoelectric coefficients from(8). According to data from Table 3 and Figure 3, and valuesof d∗h ≈ 200 pC/N are expected at 0.90 < m < 0.98 and70◦ < β < 75◦, values of |g∗h | ≈ 200 mV·m/N are predictedfor m ≈ 0.04–0.07 and 70◦ < β < 75◦ (more preferable)or for m ≈ 0.03–0.04 and β = 0◦ (less preferable becauseof the lower volume fraction m of SC). It is remarkablethat these hydrostatic parameters attain the extreme valuesin the same narrow range of the orientation angle β. Thevalue of absolute min e∗h = −77.2 C/m2 is achieved at m =0.825 and β = 83◦. Moreover, near this minimum point,conditions (10) are valid for the piezoelectric coefficients e∗3 j(Figure 4) that bring contributions into e∗h from (8). As forthe variation of the α angle (inset 1 in Figure 1) and thevolume fraction md of the 90◦ domains shown in inset 3 inFigure 1, it leads to the smaller extreme values of the effectivehydrostatic parameters from (8) and (9). In our opinion,such a suppression of the hydrostatic response in comparisonwith that at the variation of the β angle is directly connectedwith peculiarities of the elastic and piezoelectric anisotropyof the single-domain PZN-0.12PT SC.

The hydrostatic piezoelectric performance and the piezo-electric anisotropy of the studied composite based on thesingle-domain PZN-0.12PT SC is of value for specialistsmanufacturing the advanced composites with pronounced

domain effects. The results reported and discussed in thepresent paper may stimulate new studies on interrelationsbetween the electromechanical properties of anisotropiccomponents and the performance of the novel piezo-activecomposites.

Acknowledgments

The authors wish to thank professor Dr. A. E. Panich andprofessor Dr. I.A. Parinov (Rostov-on-Don, Russia), Dr. C.R. Bowen (Bath, UK), and professor Dr. P. Bisegna (Rome,Italy) for their interest in the research problems. The authorsare also grateful to Dr. C. R. Bowen (Bath, UK) for hiscareful reading of the paper of the present publication. Thiswork was partially supported by the administration of theSouthern Federal University (Project no. 11.1.09f on basicresearch), and this support is gratefully acknowledged.

References

[1] A. V. Krivoruchko and V. Yu. Topolov, “On the remark-able performance of novel 2-2-type composites based on[011] poled 0.93Pb(Zn1/3Nb2/3)O3-0.07PbTiO3 single crys-tals,” Journal of Physics D, vol. 40, no. 22, pp. 7113–7120, 2007.

[2] V. Yu. Topolov, A. V. Krivoruchko, P. Bisegna, and C.R. Bowen, “Orientation effects in 1–3 composites basedon 0.93Pb(Zn1/3Nb2/3)O-3-0.07PbTiO3 single crystals,” Ferro-electrics, vol. 376, no. 1, pp. 140–152, 2008.

[3] V. Yu. Topolov and A. V. Krivoruchko, “Orientation effectsin 2-2 piezocomposites based on (1 − x)Pb(A1/3Nb2/3)O3

−xPbTiO3 single crystals (A = Mg or Zn) ,” Journal of AppliedPhysics, vol. 105, no. 7, Article ID 074105, 7 pages, 2009.

[4] V. Yu. Topolov and A. V. Krivoruchko, “Polarization ori-entation effect and combination of electromechanical prop-erties in advanced 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 singlecrystal/polymer composites with 2-2 connectivity,” SmartMaterials and Structures, vol. 18, no. 6, Article ID 065011, 11pages, 2009.

[5] H. Cao, V. H. Schmidt, R. Zhang, W. Cao, and H.Luo, “Elastic, piezoelectric, and dielectric properties of0.58Pb(Mg1/3Nb2/3)O3-0.42PbTiO3 single crystal,” Journal ofApplied Physics, vol. 96, no. 1, pp. 549–554, 2004.

[6] R. Zhang, B. Jiang, W. Cao, and A. Amin, “Complete setof material constants of 0.93Pb(Zn1/3Nb2/3)O3-0.07PbTiO3

domain engineered single crystal,” Journal of Materials ScienceLetters, vol. 21, no. 23, pp. 1877–1879, 2002.

[7] R. Zhang, B. Jiang, and W. Cao, “Single-domain propertiesof 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 single crystals underelectric field bias,” Applied Physics Letters, vol. 82, no. 5, pp.787–789, 2003.

[8] M. Guennou, H. Dammak, and M. P. Thi, “2T domain-engineered piezoelectric single crystals: calculations and appli-cation to PZN-12%PT poled along [101],” Journal of AppliedPhysics, vol. 104, no. 7, Article ID 074102, 6 pages, 2008.

[9] R. E. Newnham, D. P. Skinner, and L. E. Cross, “Connectivityand piezoelectric-pyroelectric composites,” Materials ResearchBulletin, vol. 13, no. 5, pp. 525–536, 1978.

[10] V. Yu. Topolov and C. R. Bowen, Electromechanical Propertiesin Composites Based on Ferroelectrics, Springer, London, UK,2009.


[11] L. V. Gibiansky and S. Torquato, “On the use of homog-enization theory to design optimal piezocomposites forhydrophone applications,” Journal of the Mechanics and Physicsof Solids, vol. 45, no. 5, pp. 689–708, 1997.

[12] V. I. Aleshin, “Domain-orientation contribution into con-stants of the ferroelectric polydomain single crystal andpiezoelectric ceramic,” Zhurnal Tekhnicheskoi Fiziki, vol. 60,no. 1, pp. 179–183, 1990 (Russian).

[13] Y. Xu, Ferroelectric Materials and Their Applications, North-Holland, Amsterdam, The Netherlands, 1991.

Submit your manuscripts athttp://www.hindawi.com

ScientificaHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials

hydrostaticparametersanddomaineffectsinnovel2-2 ...downloads.hindawi.com/archive/2011/173064.pdf ·...

Documents